Graphs and Equations (HSC SSCE Mathematics Advanced): Flashcards

📚Flashcards
A Curve-Sketching Menu
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Mathematical sketch vs. accurate plot

Sketch shows main features, not every point precisely

Essential elements of any curve sketch

Intercepts, asymptotes, axis labels, scale indication

Step 0 in curve sketching menu

Simplify: use common denominator, factorise fully

Why find domain first?

Reveals discontinuities & where function exists

Even function condition

f(x)=f(x)f(-x) = f(x)

Odd function condition

f(x)=f(x)f(-x) = -f(x)

Symmetry type for even functions

Line symmetry in y-axis

Symmetry type for odd functions

Point symmetry about origin

When does vertical asymptote occur at x=ax = a?

Denominator = 0 but numerator ≠ 0

Horizontal asymptote

Function approaches constant LL as x±x \to \pm\infty

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